Sequences & series worksheet with answers

Free printable Sequences & series worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
kak​123456789

Find the sum S9 of the first 9 terms of the geometric sequence 2, 2.4, 2.88, …

a₁ = 2r = 1.2n = 9
S9 =
2.Easy
kak​123456

Find the sum S6 of the first 6 terms of the geometric sequence 1, 2, 4, …

a₁ = 1r = 2n = 6
S6 =
3.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ 2ᵏ·k!/kᵏ. Find L = lim |ak+1/ak|.

ak = 2ᵏ·k!/kᵏ
L =
4.Medium
AΣ (2/5)ᵏk = 1 … ∞BΣ k!/3ᵏk = 1 … ∞CΣ 1/k²k = 1 … ∞DΣ 1/(3ᵏ + k)k = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ (2/5)ᵏB: Σ k!/3ᵏC: Σ 1/k²D: Σ 1/(3ᵏ + k)
  1. 1A: Σ (2/5)ᵏ
  2. 2B: Σ k!/3ᵏ
  3. 3C: Σ 1/k²
  4. 4D: Σ 1/(3ᵏ + k)
5.Hard

f(x) = eˣ is approximated by its Maclaurin polynomial of degree 3 at x = 0.5. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = e0.5 = 1.649 to find the largest possible error |R₃|.

f(x) = eˣn = 3x = 0.5M = 1.649
|R₃| =
6.Hard
xyfP₄−0.5

Use the Maclaurin polynomial of degree 4 of f(x) = cos(3x) to approximate f(−0.5). Give P₄(−0.5).

f(x) = cos(3x)n = 4x = −0.5
P₄(−0.5) =

Answer key

  1. 1. S9 = 41.6
  2. 2. S6 = 63
  3. 3. L = 0.7358
  4. 4. B: Σ k!/3ᵏ
  5. 5. |R₃| = 0.004294
  6. 6. P₄(−0.5) = 0.08594

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